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Imputation of Missing Categorical Data by Maximizing Internal Consistency

Published online by Cambridge University Press:  01 January 2025

Stef van Buuren and
Jan L. A. van Rijckevorsel
Stef van Buuren*
Affiliation:
Department of Statistics, TNO Institute of Preventive Health Care, Leiden
Jan L. A. van Rijckevorsel
Affiliation:
Department of Statistics, TNO Institute of Preventive Health Care, Leiden
*
Requests for reprints should be sent to Stef van Buuren, TNO Institute of Preventive Health Care, PO Box 124, 2300 AC Leiden, THE NETHERLANDS. Email: buuren@nipg.tno.nl.
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Abstract

This paper suggests a method to supplant missing categorical data by “reasonable” replacements. These replacements will maximize the consistency of the completed data as measured by Guttman's squared correlation ratio. The text outlines a solution of the optimization problem, describes relationships with the relevant psychometric theory, and studies some properties of the method in detail. The main result is that the average correlation should be at least 0.50 before the method becomes practical. At that point, the technique gives reasonable results up to 10–15% missing data.

Keywords

missing datacorrelation ratiooptimal scaling

Information

Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 4 , December 1992, pp. 567 - 580
Copyright
Copyright © 1992 The Psychometric Society

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References

Dear, R. E. (1959). A principal component missing data method for multiple regression models (SP-86), Santa Monica, CA: System Development Corporation.Google Scholar
Fisher, W. D. (1958). On grouping for maximum homogeneity. Journal of the American Statistical Association, 53, 789–798.CrossRefGoogle Scholar
Gifi, A. (1990). Nonlinear multivariate analysis, Chichester: Wiley.Google Scholar
Gleason, T. C., Staelin, R. (1975). A proposal for handling missing data. Psychometrika, 40, 229–252.CrossRefGoogle Scholar
Greenacre, M. J. (1984). Theory and applications of correspondence analysis, New York: Academic Press.Google Scholar
Guttman, L. et al. (1941). The quantification of a class of attributes: A theory and method of scale construction. In Horst, P. et al. (Eds.), The prediction of personal adjustment (pp. 319–348). New York: Social Science Research Council.Google Scholar
Hartigan, J. A. (1975). Clustering algorithms, New York: Wiley.Google Scholar
Hartley, H. O., Hocking, R. R. (1971). The analysis of incomplete data. Biometrics, 27, 783–808.CrossRefGoogle Scholar
Kalton, G., Kasprzyk, D. (1982). Imputing for missing survey responses. Proceedings of the Section of Survey Research Methods, 1982 (pp. 22–23). Alexander, VA: American Statistical Association.Google Scholar
Little, R. J. A., Rubin, D. B. (1990). The analysis of social science data with missing values. In Fox, J., Scott Long, T. (Eds.), Modern methods of data analysis (pp. 374–409). London: Sage.Google Scholar
Madow, W. G., Olkin, I., Rubin, D. B. (1983). Incomplete data in sample surveys, New York: Academic Press.Google Scholar
Meulman, J. (1982). Homogeneity analysis of incomplete data, Leiden: DSWO Press.Google Scholar
Milligan, G. W. (1980). An examination of the effect of six types of error perturbation of fifteen clustering algorithms. Psychometrika, 45, 325–342.CrossRefGoogle Scholar
Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its applications, Toronto: University of Toronto Press.CrossRefGoogle Scholar
Nishisato, S., & Ahn, H. (in press). When not to analyze data: Decision making on missing responses in dual scaling. Annals of Operations Research.Google Scholar
Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys, New York: Wiley.CrossRefGoogle Scholar
Rubin, D. B. (1991). EM and beyond. Psychometrika, 56, 241–254.CrossRefGoogle Scholar
Scheibler, D., Schneider, W. (1985). Monte Carlo tests of the accuracy of cluster analysis algorithms. Multivariate Behavioral Research, 20, 283–304.CrossRefGoogle ScholarPubMed
Späth, H. (1985). Cluster dissection and analysis, Chichester: Ellis Horwood.Google Scholar
Tanner, M. A., Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 528–550.CrossRefGoogle Scholar
van Buuren, S., Heiser, W. J. (1989). Clustering n objects into k groups under optimal scaling of variables. Psychometrika, 54, 699–706.CrossRefGoogle Scholar
van Buuren, S., van Rijckevorsel, J. L. A. (1992). Data augmentation and optimal scaling. In Steyer, R., Wender, K. F., Widaman, K. F. (Eds.), Psychometric Methodology. Proceedings of the 7th European Meeting of the Psychometric Society in Trier (pp. 80–84). Stuttgart and New York: Gustav Fischer Verlag.Google Scholar
van der Heijden, P. G. M., & Escofier, B. (1989). Multiple correspondence analysis with missing data. Unpublished manuscript, University of Leiden, Department of Psychometrics and Research Methods.Google Scholar
van Rijckevorsel, J. L. A., & de Leeuw, J. (1992). Some results about the importance of knot selection in nonlinear multivariate analysis. Statistica Applicata: Italian Journal of Applied Statistics, 4.Google Scholar